The Hamiltonian structure of the expanding integrable model of the generalized AKNS hierarchy

With the help of a new loop algebra g˜, a simple deducing method for the generalized AKNS hierarchy (briefly called GAH) is given. Then, g˜ is extended to a larger loop algebra G∼ from which the integrable couplings of the GAH, i.e. a kind of expanding integrable model, is obtained. It follows that its Hamiltonian structure is worked out by making use of the quadratic-form identity. Finally, a subalgebra a˜3 of the loop algebra A∼3 is devoted to getting the conserved densities of the integrable couplings by the HAKS algorithm.